In games such as billiards and shuffleboard, a rigid body is propelled to collide with another rigid body, in order to direct one or both of the bodies to desired locations. In pocket billiards, for example, a cue ball is struck by a cue stick and propelled toward an object ball. The collision between the cue ball and the stationary object ball is designed to cause the object ball to travel in a desired trajectory, such as that leading to a billiard table pocket. At the same time, the collision between the two balls typically must be designed so that the cue ball does not travel into any of the billiard table pockets.
While it may seem easy in principle to aim a cue ball to collide with an object ball at the correct location to cause desired post-collision trajectories of cue and object balls, in practice it is not always easy. One problem is that errors in the direction the cue ball travels to strike the object ball relative to the direction aimed are not easily distinguishable from errors in aiming the cue ball. That is, the person playing pool may not know whether he or she missed a shot due to aiming incorrectly or due to aiming correctly but addressing the cue ball incorrectly with the cue stick. Similarly, aiming incorrectly may, in combination with striking the cue ball erroneously with the cue stick, result in a successful shot. This confusion thwarts the progress of players and prolongs the period required for training.
Several patents have addressed the issue of aiming objects such as billiard balls. U.S. Pat. No. 3,993,305 to Nicholson discloses a billiard ball that is patterned to help train billiard players to aim using a system known as "sighting by object ball displacement." In this method, a training ball is provided that has stripes extending between two opposed poles. The ball is positioned on the table as an object ball and has its poles vertically aligned and its stripes aligned with the desired trajectory. That is, it is manually rotated to where one pole is in contact with the table and the other pole is at the top of the ball, and a stripe is aligned to be on the opposite side of the ball from the desired trajectory of the object ball. Next, it is determined whether the desired shot is a "thin-ball", "quarter-ball", "half-ball" or "full-ball". Then the training ball is sighted from behind the cue ball so that the cue ball obstructs from view a fraction of the training ball corresponding to the type of shot it has been determined to be. For example, for a "quarter-ball "shot, one quarter of the training ball is obstructed from view by the cue ball. The cue ball is then aimed in a direction parallel to that between an edge of the cue ball and the desired visually obstructed fraction of the training ball.
Similarly, U.S. Pat. No. 3,711,091 to Dixon describes a pointing apparatus which may be placed on the pool table playing surface or the railing surrounding the playing surface and which indicates the desired trajectory of the object ball. The apparatus generally includes a pair of imitation pool balls attached to each other and to a pointer shaft and mounted on a foundation. A more modern approach to aiming in billiards is disclosed in U.S. Pat. No. 4,68.8,796 to Wright, which describes a cue stick having a collimated beam of light that can be activated to project from its tip. The beam of light can be used to help aim the cue stick at the cue ball, the cue ball at the object ball and, when augmented by reflective strips attached to the table railing, the cue or object ball at targets to be struck by banking the balls off of the railing.
In a somewhat similar vein, U.S. Pat. No. 3,917,264 to Davidson et al. describes a billiard table area that is illuminated with a source of invisible, ultraviolet light, and pool balls and playing devices that are coated with a material that emits visible light when exposed to such ultraviolet light, thereby providing the illusion that the balls are floating on an invisible plane. The ultraviolet light can be pulsed to create a stroboscopic effect, which is claimed to be an aid to aiming the balls.
The above referenced patents indicate the need for aiming systems with billiards and other games. A need still exists for providing an exact location to aim a cue ball at in order to propel an object ball in an arbitrary desired trajectory.